Autoregressive Integrated Moving Average (ARIMA) modeling is a statistical technique used for time series data in order to understand and forecast future trends in a better way. Recently, the ARIMA models have been employed in practice for modeling the data of total fisheries production in India. In this study, an important family of parametric time series modeling when the order of difference is fractional, called Autoregressive Fractional Integrated Moving Average (ARFIMA), has been proposed for modeling and forecasting the total fisheries production (metric tons) in India. For testing the fundamental assumption of stationarity, Augmented Dickey Fuller (ADF) test was used. We also used a nonparametric model such as Neural Network Autoregressive (NNAR) for investigating the behavior of the data. After the evaluation of different models and perform comparisons based on root mean square error(RMSE) and mean absolute percentage error (MAPE) values, the result indicated that ARFIMA (3, 0.48,0), ARIMA(1,2,1) and NNAR(3,1) were the best models. The current results reflected that ARFIMA model outperformed ARIMA and NNAR models in forecasting the total fisheries prediction. This could be suggested that the ARFIMA might be a remarkable selection for time series data modeling.